MB · The Lab

EXP. 003 · Strange Loop

Steps 0 · net distance 0 — you are where you began

The Lab — EXP. 003 · after Gödel, Escher, Bach

A page that contains this page.

The frame holds a live picture of the whole view — frame, thread, and all. Scroll or drag down to descend into it; every level arrives where you began, like the canon that rises through its keys back to C. Drag sideways to twist the regress into a spiral.

EXP. 003 — Notes

Strange Loop

A camera is pointed at its own output: each finished frame is fed back in as a texture, rotated and shrunk by a fixed amount, and drawn inside the next. Iterate any starting image under a contracting transform and it converges to the one image the transform leaves unchanged — the fixed point. That's what stabilizes on screen: a picture made of nothing but itself. The endless zoom works because every level is self-similar, the visual form of a canon that rises forever without leaving its key.

A growth loop is defined by its transform, not its content: the operation applied every cycle. Invites bring users who send invites; content earns search traffic that funds content. Whatever you seed it with, repetition converges to the shape the transform allows — the steady state is a property of the loop, not the launch.

So debug the operation, not the instance. Improve one step's conversion and the fixed point moves everywhere at once. And run the series: a loop factor near 1 compounds into something enormous; at 0.5 the whole future of a seed is only 2× the seed.

Descend forever and arrive where you began. The frame holds a picture of the frame holding a picture, and somewhere in the regress the content stops mattering — what survives is the rule. Every self-referential system keeps only what its transform can carry.

  1. Mechanism under test: real video feedback — each frame renders the room, then composites the PREVIOUS full frame inside the specimen frame under T = rotate(θ)·scale(1/k). The image on screen is the fixed point of its own transformation: run the loop and the infinite regress simply appears, by contraction.
  2. The zoom is a canon per tonos: descending by one full level lands on an identical view, so the descent wraps seamlessly — you can fall (or rise) forever. The step counter is real and monotonic; the net distance is honestly zero. That contradiction is the exhibit.
  3. One thread through all levels: each level's vermillion thread is drawn to END exactly where T places the NEXT level's beginning, so the composite is a single unbroken line spiraling through the whole hierarchy — a tangled hierarchy you can trace with a finger.
  4. Twist: dragging sideways changes θ, and the entire existing regress re-corkscrews to the new fixed point over a few frames — you can watch the hierarchy renegotiate itself.
  5. What might graduate: possibly nothing — some loops are for standing in. If anything: the fixed-point compositing trick, and the descent-wrap grammar. (Seeded for a later number, the other half of the ask: n-dimensional space — the tesseract room, 4-D rotation under your pointer.)

PHYSICS — raw WebGL2, RGBA8 feedback ping-pong (no float textures needed), no libraries, single file · loop runs only while converging or while zoom/twist velocity > ε, then stops — zero idle frames, visibility-gated · reduced motion = the converged still, loop not driveable · no-GL = designed fallback · zero console errors · wheel zooms only over the loop; the page keeps its native scrollbar and skip link.

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